I. Ketil. Western University of Health Sciences.
A great change in aesthetic surgery operative techniques has taken place after the Second World War and in recent years order generic amitriptyline canada depression of 1893. Correction of upper and lower blepharoplasty became more precise and sophisti- cated generic amitriptyline 10mg line depression symptoms hair loss. A good review of the literature on blepharoplasty and cosmetic surgery is supplied by Dupuis and Rees [34 ] buy amitriptyline 25mg with mastercard depression cherry stream, Fig. Hunt for upper and lower eyelid correction in 1926  History of Cosmetic Eyelid Surgery 729 a b c Fig. Nöel for upper and lower eyelid correction (From: La Chirurgie Esthétique (1926)  ) a b Fig. Published Wien kl Wochenschr 9:109–110 in facsimile and hieroglyphic transliteration with translation and 23. The correction of featural a venerabili D’Hanvantare demonstratum a Susruta discipulo com- imperfections, 2nd edn. Lascaratos J, Cohen M, Voros D (1998) Plastic surgery of the Paris face in Byzantium in the fourth century. Bourguet J (1928) Notre traitement chirurgical de « poches » sous 1274–1280 les yeux sans cicatrice. Technique et century encyclopedist and surgeon: his role in the history of plastic Résultats. Kestenbaum A (1935) Modiﬁcation of ectropion operation accord- ing to Kuhnt-Szymanowski procedure. Klin Montatsbl f Augenheilk 95:51–53 Anatomy of the Orbitopalpebral Region Paolo Persichetti , Stefania Tenna , and Annalisa Cogliandro 1 Introduction medial third and middle third of the upper edge is located the supraorbital foramen through which pass the external frontal The orbitopalpebral region is a complex anatomofunctional nerve – also named supraorbital nerve – and the supraorbital unit, formed by several structures to support, protect, and artery. In the middle part of the lower edge there is the infra- assist the eye in performing the visual function. This chapter aims to point out the anatomical basis of the orbitopalpebral region and systematically give the new morphological concepts whose knowledge has become of great signiﬁcance for a correct surgical approach. Its base corresponds with the anterior opening; it has a quadrangular shape and consists of the fron- tal bone at the top, the orbital part of the maxillary bone at the bottom and the inner side, and the zygomatic bone at the bottom and the outer side. The optic nerve together with the oph- and the greater wing of the sphenoid ; ﬁnally the inner or thalmic artery, which is located below and lateral to the nerve nasal wall constituted forward reverse by the orbital part of itself, passes through these structures. The orbit is also related in the upper part with the anterior 3 Eyeball cranial fossa, at the back with the middle cranial fossa and the sphenoid sinus, inferiorly with the maxillary sinus, later- The eyeball has an ovoid shape to the most anteroposterior ally with the temporal fossa and medially, through the eth- axis and occupies the anterior prefascial portion of the orbital moidal cells, with the nasal cavity. It adheres to the posterior hemi- the greater wing of the sphenoid that gives passage to the sphere of the eyeball and separates it from the adipose body frontal, lacrimal, trochlear, common oculomotor, abducens of the orbit; it extends forward, behind the conjunctival for- nerves, to the nasociliary branch of the ophthalmic nerve, the nix, until the sclerocorneal margin and backwards it wraps sympathetic root of the ciliary ganglion and to the upper and around the optic nerve. It is connected to the edges of the lower ophthalmic veins; and the inferior orbital ﬁssure or orbit by means of a funnel-shaped extension through the sphenomaxillary between the orbital portions of the maxilla, peribulbar adipose tissue. This connective funnel-shaped tis- the greater wing of the sphenoid and the zygomatic bone that sue, thanks to a non-uniform thickness, very thin in some gives passage to the zygomatic nerve, the maxillary nerve, points, allows the passage of the neurovascular structures the orbital branches of the sphenopalatine ganglion, as well anteriorly. The capsule has a special relationship with the as to an anastomosis between the inferior ophthalmic vein ocular muscles forming a sheath such as a ﬁnger glove for and the venous pterygoid plexus (Figs. These sheaths, more developed forward, Finally in the posterior side of the orbit at its apex, is located thinner and transparent behind, are connected by a very thin the optic foramen followed by the optic canal, which has close connective lamella in the peribulbar portion called Anatomy of the Orbitopalpebral Region 735 Fig. It goes sideways, backward, and upward, all contained in the orbital cavity and are classiﬁed into two describing a loop around the eyeball and folding obliquely groups: the rectus muscles (superior, inferior, lateral, and from below the inferior rectus muscle, so that the two sheaths medial) and the oblique ones (upper and lower) (Fig. The most developed stretched, ribbon-shaped muscles, narrower behind, and arrest tendon is the lateral rectus muscle, which joins on the wider forward where by means of a long, ﬂattened tendon, outer wall of the orbit at the level of the lateral retinaculum thin and wider than the muscular body, attach themselves to near the tubercle of Whitnall. The biggest tendon of the medial rectus muscle is inserted on the poste- and strongest is the medial rectus. The insertion line of the rior lacrimal crest, behind the deep insertion of the medial rectus muscles is called spiral of Tillaux. The superior rectus muscle has two There are two oblique muscles: the upper one is the lon- orbital tendons that arise from the medial and lateral edge of gest and thinnest of the ocular muscles; it arises with a short its sheath and are inserted in the upper, medial, and lateral tendon from the medial edge of the optic foramen and the corners of the orbit. They also send numerous ﬁbers to the optic nerve sheath and is linked at the top of the orbit with tarsus and the conjunctival fornix mingling in part with the the insertion of the levator muscle of the upper eyelid. In collateral expansions of the levator muscle tendon of the eye- proximity of the base of the orbital pyramid it is transformed lid (Fig. These relationships justify a sort of functional into a cylindrical tendon that joins a ﬁbrocartilagineous eye- solidarity between the superior rectus muscle and elevating let, the trochlea , ﬁxed to the dimple or the trochlear spine of muscle of upper eyelid strengthened by the merger of the the frontal bone, where it is reﬂected to head sideways and sheaths of the two muscles, and explain why the upper lid is back towards the eyeball inserting on the sclera, in the super- lifted, when the superior rectus muscle is contracted making olateral part of the posterior hemisphere of the eye. It arises from the anteromedial part of inferior oblique muscle, the sheath of the two muscles the lower wall of the orbit in the jawbone below the fossa of appears thickened and sends prolongations towards the walls 736 P. The main functions of the intraorbital adipose tissue are those of protection, sup- port, and reduced friction of the eyeball. The numerous lob- ules in which the fat is subdivided by thin ﬁbrous septa, are oriented along the axis of movement of each connected structures, thereby creating spaces of ﬂowing (e. These ﬁbrous septa are not independent of each other but they proceed and are in continuity with the ﬁbrous sheaths that cover the mus- cles and the globe (Tenon’s capsule, capsulopalpebral fas- cia); inside the septa there are small artery and veins. The division of the adipose tissue by these ﬁbrous septal forma- tions enables it to modify its own shape in the presence of a constant volume. This arrangement also determines the for- mation of the adipose compartments of the eyelids. They are commonly divided into tus, and levator muscle of the eyelid upper and lower. Each eyelid is anatomically divided into two lamellae, one posterior and one anterior to the axis that of the orbit to form the lower transverse ligament (or suspen- passes through it and connects the orbital septum and the sory Lockwood’s ligament). The arrangement brae superioris muscle and the inferior retractors, as well as of these thickenings and extensions of the sheaths of muscles the conjunctiva of the inner lining. The eyelid skin is the thinnest of the human body (<1 mm), it is more delicate than the surrounding tissues and due to aging tends to atrophy losing elasticity and ﬁrmness. The 4 Adipose Body of the Orbit medial or nasal portion is characterized by numerous seba- ceous glands and poor hair formations, pointing out the tran- Adipose body of the orbit is the name of the lobular mass of sition with the eyebrow skin superiorly and the cheek adipose tissue that ﬁlls the so-called retrofascial loggia of the inferiorly. The adipose body of the orbit is third; adipose elements are rare and totally absent at the level crossed by the ocular muscles, surrounded by their sheaths, of the pretarsal subcutaneous tissue. The same subcutaneous by the vessels and nerves of the orbit and takes relationship tissue lacks at the medial and lateral palpebral ligaments, with the capsule that encloses the lacrimal gland. The main where there is a close connection of the skin with the under- mass of the adipose body is contained in the pyramidal space lying ﬁbrous tissue. The dermis, resulting in facial expressions that characterize the sinking of the eye cannot go beyond a certain limit because mankind. The muscle can be divided in a central or palpebral Anatomy of the Orbitopalpebral Region 737 frontal bone; it widely extends in a circular way around the orbit (such as a horseshoe), connecting with the other mus- cles of facial expression (frontal muscle, corrugator, procer- ous, major and minor zygomatic muscles), and extends laterally to cover the superﬁcial temporal fascia. The preseptal portion of the orbicularis muscle lies super- ﬁcially to the eyelid orbital septum and its median origin consists of a superﬁcial end and a deep one associated with the medial palpebral ligament. The ﬁbers coming from the upper and lower eyelid combine laterally forming the lateral palpebral raphe, adherent to the overlying skin. The pretarsal portion is located at the front of the tarsus to the free margin of the eyelid, and its two heads of origin (superﬁcial and deep) are intimately associated to form the medial palpebral ligament.
It is estimated that only about half (51%) of all bladder injuries 1561 are identified and repaired intraoperatively  buy amitriptyline with a mastercard mood disorder care plan. Unfortunately safe amitriptyline 10 mg anxiety upon waking, the true incidence of urogenital fistula after peer- reviewed data is sparse best order amitriptyline depression verses, largely comprised of case reports. Ureterovaginal Fistulas Ureterovaginal fistulas are rare complications that are often caused by unrecognized injury to the ureter during pelvic surgery. Considered one of the most serious complications in pelvic surgery, consequences include paralytic ileus, sepsis, renal failure, and renal loss [13,16]. Although the ureter can be injured during any pelvic surgery, injury occurs most commonly during gynecological operative procedures. Approximately 60%–75% of ureterovaginal fistulas developed as a result of ureteral injuries during abdominal hysterectomy [50,51]. In the literature, the incidence of ureteral injury during hysterectomy ranges from 0. The incidence of concomitant vesicovaginal and ureterovaginal fistula has been reported to be as high as 12%–25% [6,52,53]. Ureterovaginal fistulas are less common in the developing world but have been described in the obstructed labor complex . The ureter is at greatest risk of iatrogenic injury in the distal third centimeters. It is most commonly injured during its course over the pelvic brim, through the cardinal ligament, near the uterosacral ligament, and at the level of the vaginal fornix prior to insertion into the bladder . The left ureter is at greatest risk of injury due to its course in the pelvis, which places it closer to the cervix than the right ureter [31,55]. However, right-sided injuries are still common and have been reported to occur more frequently in another small series . Ureterovaginal fistulas can occur as a result of partial versus complete ureteral transection, electrocautery, or ischemic injury caused by suture ligation, clamp trauma, or damage to the delicate periureteral blood supply [6,16]. The complex fistulous connections that can develop are often difficult to define due to their tortuosity and proximity to the ureterovesical junction . A missed ureteral injury can be disastrous and should always be ruled out during the diagnostic evaluation of any patient with suspected urogenital fistula. Other rare causes of ureterovaginal fistulas include retained vaginal foreign bodies (i. Over 70% are associated with anti-incontinence surgery, anterior colporrhaphy, and urethral diverticulectomy [11,12,14,59]. Inadvertent urethral injury during paraurethral dissection and/or trocar passage of urethral slings may cause erosion, tissue loss, and subsequent urethrovaginal fistula . Iatrogenic urethrovaginal fistulas have become more common since the adoption of synthetic midurethral slings and mesh kits [32,60–66]. Almost 40% were associated with pelvic organ prolapse repair and urethral diverticulectomy. Ureterovaginal fistulas can also coexist, so the clinician should make sure to rule out all possible fistulous connections. Other less 1562 common but important causes include malignancy, pelvic trauma, pelvic radiation, and chronic indwelling urethral catheters [45,59]. Any patient with a history of malignancy or pelvic irradiation should undergo biopsy to rule out malignancy. Vesicouterine Fistulas Vesicouterine fistulas are one of the least common urogenital fistulas, representing 1%–9% of all urogenital fistulas [30,33,41]. They are most commonly associated with lower uterine segment cesarean section [5,19,31–33,40]. Women with vesicouterine fistulas often present with a constellation of symptoms referred to as Youssef’s syndrome, characterized by cyclical hematuria (menouria), amenorrhea (absence of vaginal bleeding), first trimester spontaneous abortions, and absence of urinary incontinence [33,69]. Vaginal urinary incontinence can also be present and is most likely caused by retrograde filling of the uterus with urine from the bladder and subsequent leakage from a patent, incompetent cervical os . Amenorrhea and menouria (cyclical hematuria) may develop as a result of the fistulous communication between the bladder and uterus. The mixture of menstrual blood from the uterus with urine in the bladder manifests as gross hematuria (menouria) that only occurs during the menstrual cycle. As many as 20%–25% of patients with bladder endometriosis involving the bladder mucosa present with cyclical hematuria . Thus, the clinician must rule out other potential causes of cyclical hematuria, including endometriosis and congenital anomalies [68,69]. Similar to vesicouterine fistulas, they have been described in patients after cesarean section [71,72], underscoring the importance of ruling out concomitant fistulas. Ureterofallopian Fistulas Ureterofallopian fistulas are exceedingly rare urogenital fistulas . Only six have ever been described in the literature, all of which were iatrogenic, attributed to pelvic gynecological surgery for endometriosis [13,15–17], malignancy , and urological endoscopic treatment of ureteral stones [5,20,21]. The evaluation must begin with basic diagnostic principles of a thorough history and physical examination. This may confirm the clinician’s suspicion, but additional testing is most often required to confirm the diagnosis, understand the fistula anatomy, and rule out concomitant injuries (Figure 106. The information gained is critical to staging appropriate corrective interventions, which will be discussed in the next chapter. In this section, we will discuss the presentation and diagnostic tools that are available to the clinician for the workup of a patient with suspected urogenital fistula. History In any patient with a suspected urogenital fistula, the evaluation should begin with a detailed medical, surgical, obstetrical, gynecological, oncological, and social history. The clinician must characterize the urinary leakage and differentiate it from other potential causes of urinary incontinence. The patient should be asked to describe the fluid character, color, volume, onset of leakage, and the position during which leakage typically occurs. Other conditions of the lower urinary tract, including urgency incontinence, stress incontinence, mixed urinary incontinence, vaginal voiding, and overflow incontinence, can mimic the classic presenting symptoms of urogenital fistulas. However, if a fistula is suspected based on the presence of patient risk factors, it must be ruled out. The patient’s past surgical history should be reviewed, including prior pelvic trauma or radiation. In cases of prior abdominal and pelvic surgery, the surgeon’s operative notes should be obtained. The obstetrical history, including number of pregnancies, deliveries, and mode of deliveries (vaginal, vacuum assisted, forceps, cesarean) should be reviewed. Any history of gynecological, urological, or colorectal malignancies and subsequent treatments should also be noted. Pathology reports and surgical and/or radiation treatment reports should be obtained. Smoking cessation should be strongly encouraged in order to improve the chances of surgical success. As the clinician completes this detailed history, the differential diagnosis for continuous vaginal fluid drainage should be kept in mind.
Cytokeratin 20 immunoreac- tivity distinguishes Merkel cell (primary cutaneous neuroendocrine) carcinomas and salivary gland small cell carcinomas from small cell carcinomas of various sites order amitriptyline 25mg with visa depression help tumblr. Myoepithelial carcinoma of the salivary glands: a clinicopathologic study of 25 patients discount generic amitriptyline canada vasomotor depression definition. Fine-needle aspiration cytology of lymphoprolifera- tive lesions involving the major salivary glands amitriptyline 50mg online mood disorder and suicide. Chapter 8 Ancillary Studies for Salivary Gland Cytology Marc Pusztaszeri, Jorge S. Reis-Filho, Fernando Carlos de Lander Schmitt, and Marcia Edelweiss General Background A precise cytologic classifcation of salivary gland tumors based on cytomorphology alone is possible for many of the commonly encountered lesions; however, there are challenges for the cytologic diagnosis of some entities. A subset of tumors has been charac- terized cytogenetically by the presence of specifc and recurrent translocations (see Table 10. Most of these methods can be readily integrated into the diagnostic workfow, particularly as they become more widely available, cost-effective, and effcient with shorter turnaround times [3, 4]. Cell blocks have the advantage of being analo- gous to paraffn tissue blocks, with minimal need of standardization and with reliable results. Special Stains Histochemical stains are often used to highlight stromal or cytoplasmic compo- nents. These stains also detect intracytoplasmic mucin, which can be found in a 8 Ancillary Studies for Salivary Gland Cytology 141 Fig. Oil Red O remains one of the best stains to confrm sebaceous dif- ferentiation by highlighting lipid droplets in unfxed cells. Immunochemistry for Basaloid Neoplasms Aspirates of basaloid neoplasms present a very broad and challenging differential diagnosis (see Chap. In addition, clear cell carcinoma is a rare low-grade salivary gland carcinoma that is often positive for p63, but lacks myoepithelial differentiation and also lacks intracellular mucin . Epithelial- myoepithelial carcinoma is characterized by a predominant population of myoepi- thelial cells displaying an unusually large amount of clear cytoplasm. Pancytokeratin immunostain showing the biphasic pattern of the tumor Immunochemistry for Primary vs. Secondary Salivary Gland Tumors High-grade carcinomas in the salivary glands are usually easily recognized as malignant; however, the distinction between primary and secondary malignancy can occasionally be problematic yet clinically important. Most patients with a secondary malignancy of the salivary gland have a clinical history. The most common distant metastases to the salivary gland are lung, breast, and kidney (see Table 8. In addition to their diagnostic role, in some cases these genetic trans- locations can also represent prognostic markers and therapeutic targets [1, 2]. The presence of this translocation is also associated with fewer recurrences, metastases, and tumor-related mortality. The use of cytological material has the advantage of not having truncated nuclei due to sectioning, but cell-blocks can also be used with the same adaptations used for histological sections. Dual-observer scoring is recommended due to the intraobserver and interobserver variations, and use of internal and external quality controls are strongly advised. For B-cell lymphomas, the demonstration of a clonal population based upon the presence of kappa or lambda light chain restriction as well expression of Bcl2 is diagnostic. The presence of an altered T-cell immunophenotype also can be used to suggest a possible T-cell lymphoma. This immunoprofle combined with the cytomorphologic fndings favors a diagnosis of pleomor- phic adenoma. Combined with the cytomorphologic fnd- ings, the features are suspicious for adenoid cystic carcinoma. Combined with the cyto- morphologic fndings, the overall features are consistent with acinic cell carcinoma. Note: The combined cytomorphologic fndings and benign fow cytometry favor a reactive lymph node. If lymphadenopathy persists, repeat sampling would be indicated for further evaluation. The landscape of gene fusions and somatic mutations in salivary gland neoplasms—implications for diagnosis and therapy. Update in salivary gland cytopathology: recent molecular advances and diagnostic applications. New developments in salivary gland pathology: clinically useful ancillary testing and new potentially targetable molecular altera- tions. Ancillary testing strategies in salivary gland aspiration cytology: a practical pattern-based approach. Usefulness of translocation-associated immunohistochemical stains in the fne-needle aspiration diagnosis of salivary gland neoplasms. Use of fuores- cent in-situ hybridisation in salivary gland cytology: a powerful diagnostic tool. Fine-needle aspiration cytology of lymphoid lesions of the salivary gland: a review of 35 cases. Flow cytometry signifcantly improves the diagnostic value of fne needle aspiration cytology of lymphoprolif- erative lesions of salivary glands. Next-generation sequencing in salivary gland basal cell adenocarcinoma and basal cell adenoma. Mammary analogue secre- tory carcinoma of parotid: is preoperative cytological diagnosis possible? Diagnostic utility of phosphorylated signal transducer and activator of transcription 5 immunostaining in the diag- nosis of mammary analogue secretory carcinoma of the salivary gland: a comparative study of salivary gland cancers. Salivary duct carcinoma cytologically diagnosed distinctly from salivary gland carcinomas with squamous differentiation. Polymorphous low grade adenocarcinoma has a consistent p63+/p40- immunophenotype that helps distinguish it from adenoid cystic carcinoma and cel- lular pleomorphic adenoma. Varvares General Background The heterogeneity of salivary gland disease presents unique challenges for the pathologist, radiologist, and treating clinician in their pursuit of optimal patient care. Cytomorphology is able to provide valuable information regarding the nature of the salivary gland lesion. Because of signifcant morphologic overlap of some entities, it is unavoidable that at times only a morphological description of the M. Nicolai Otorhinolaryngology–Head and Neck Surgery, University of Brescia, Brescia, Italy e-mail: pieronicolai@virgilio. This mandates that a clear line of communication exists between cytopathologist and the treating clinician to ensure that the patient receives the correct management. It is in this context that a uniform reporting system for salivary gland cytology is most benefcial.
Suppose we have 16 subjects available to participate in an experiment in which we wish to compare four drugs buy amitriptyline overnight delivery anxiety burning sensation. We then go to a table of random numbers and select 16 consecutive order generic amitriptyline canada mood disorder blogs, unduplicated numbers between 01 and 16 generic amitriptyline 10mg without a prescription depressive symptoms definition. To illustrate, let us use Appendix Table A and a random starting point that, say, is at the intersection of Row 4 and Columns 11 and 12. The succeeding (moving downward) 16 consecutive two-digit numbers between 01 and 16 are 16, 09, 06, 15, 14, 11, 02, 04, 10, 07, 05, 13, 03, 12, 01, and 08. We allocate subjects 16, 09, 06, and 15 to drug A; subjects 14, 11, 02, and 04 to drug B; subjects 10, 07, 05, and 13 to drug C; and subjects 03, 12, 01, and 08 to drug D. We emphasize that the number of subjects in each treatment group does not have to be the same. The measurements (or observations) resulting from a completely randomized experimental design, along with the means and totals that can be computed from them, may be displayed for convenience as in Table 8. Before stating the assumptions, let us specify the model for the experiment described here. The Model As already noted, a model is a symbolic representation of a typical value of a data set. To write down the model for the completely randomized experimental design, let us begin by identifying a typical value from the set of data represented by the sample displayed in Table 8. Components of the Model By looking at our model we can see that a typical observation from the total set of data under study is composed of (1) the grand mean, (2) a treatment effect, and (3) an error term representing the deviation of the observation from its group mean. In most situations we are interested only in the k treatments represented in our experiment. When we place such a restriction on our inference goals, we refer to our model as the fixed-effects model,or model 1. Assumptions of the Model The assumptions for the fixed-effects model are as follows: (a) The k sets of observed data constitute k independent random samples from the respective populations. P (d) The tj are unknown constants and tj ¼ 0 since the sum of all deviations of the mj from their mean, m, is zero. We test the null hypothesis that all population or treatment means are equal against the alternative that the members of at least one pair are not equal. If the population means are equal, each treatment effect is equal to zero, so that, alternatively, the hypotheses may be stated as H0 : tj ¼ 0; j ¼ 1; 2;... When H0 is true the population means are all equal, and the populations are centered at the same point (the common mean) on the horizontal axis. If the populations are all normally distributed with equal variances the distributions will be identical, so that in drawing their pictures each is superimposed on each of the others, and a single picture sufficiently represents them all. When H0 is false it may be false because one of the population means is different from the others, which are all equal. The test statistic for one-way analysis of variance is a computed variance ratio, which we designate by V. The methods by which they are calculated will be given in the discussion that follows. In general, the decision rule is: reject the null hypothesis if the computed value of V. We have defined analysis of variance as a process whereby the total variation present in a set of data is partitioned into components that are attributable to different sources. The term variation used in this context refers to the sum of squared deviations of observations from their mean,orsum of squares for short. Those who use a computer for calculations may wish to skip the following discussion of the computations involved in obtaining the test statistic. The Total Sum of Squares Before we can do any partitioning, we must first obtain the total sum of squares. The total sum of squares is the sum of the squares of the deviations of individual observations from the mean of all the observations taken together. The Within Groups Sum of Squares Now let us show how to compute the first of the two components of the total sum of squares. The first step in the computation calls for performing certain calculations within each group. These calculations involve computing within each group the sum of the squared deviations of the individual observations from their mean. When these calculations have been performed within each group, we obtain the sum of the individual group results. It can be shown that when the assumptions are met and the population means are all equal, both the among sum of squares and the within sum of squares, when divided by their respective degrees of freedom, yield independent and unbiased estimates of s2. The First Estimate of s2 Within any sample, Xnj ÀÁ2 xij À x:j i¼1 nj À 1 provides an unbiased estimate of the true variance of the population from which the sample came. The student will recognize this as an extension to k samples of the pooling of variances procedure encountered in Chapters 6 and 7 when the variances from two samples were pooled in order to use the t distribution. It is not necessary, however, for H0 to be true in order for the within groups mean square to be a valid estimate of s2; that is, the within groups mean square estimates s2 regardless of whether H is true or false, as long as the population variances 0 are equal. If we solve this x equation for s2, the variance of the population from which the samples were drawn, we have 2 2 s ¼ nsx (8. This sum of squares when divided by the associated degrees of freedom k À 1 is referred to as the among groups mean square. If the null hypothesis is false, that is, if all population means are not equal, we would expect the among groups mean square, which is computed by using the squared deviations of the sample means from the overall mean, to be larger than the within groups mean square. Both conditions, a true null hypothesis and equal population variances, must be met in order for the among groups mean square to be a valid estimate of s2. If, on the other hand, the among groups mean square is considerably larger than the within groups mean square, V. We know that because of the vagaries of sampling, even when the null hypothesis is true, it is unlikely that the among and within groups mean squares will be equal. We must decide, then, how big the observed difference must be before we can conclude that the difference is due to something other than sampling fluctuation. The F Test To answer the question just posed, we must consider the sampling ÀÁdistribution of the ratio of two sample variances. In Chapter 6 we learned that the quantityÀÁ s2=s2 = s2=s2 follows a distribution known as the F distribution when the sample 1 1 2 2 variances are computed from random and independently drawn samples from normal populations. Fisher in the early 1920s, has become one of the most widely used distributions in modern statistics. We have already become acquainted with its use in constructing confidence intervals for, and testing hypotheses about, population variances. In this chapter, we will see that it is the distribution fundamental to analysis of variance. It is of interest to note that the F distribution is the ratio of two Chi-square distributions.